Solve for $x$ and $y$ using elimination. ${-2x-6y = -30}$ ${2x-5y = -14}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-11y = -44$ $\dfrac{-11y}{{-11}} = \dfrac{-44}{{-11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-2x-6y = -30}\thinspace$ to find $x$ ${-2x - 6}{(4)}{= -30}$ $-2x-24 = -30$ $-2x-24{+24} = -30{+24}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 4}$ into $\thinspace {2x-5y = -14}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(4)}{= -14}$ ${x = 3}$